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Normal systems over ANR’s, rigid embeddings and nonseparable absorbing sets

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Abstract

Most of results of Bestvina and Mogilski [Characterizing certain incomplete infinite-dimensional absolute retracts. Michigan Math. J., 33, 291–313 (1986)] on strong Z-sets in ANR’s and absorbing sets is generalized to nonseparable case. It is shown that if an ANR X is locally homotopy dense embeddable in infinite-dimensional Hilbert manifolds and w(U) = w(X) (where “w” is the topological weight) for each open nonempty subset U of X, then X itself is homotopy dense embeddable in a Hilbert manifold. It is also demonstrated that whenever X is an AR, its weak product W(X, *) = {(x n ) ∞n=1 ∈ X ω: x n = * for almost all n} is homeomorphic to a pre-Hilbert space E with E ≅ ΣE. An intrinsic characterization of manifolds modelled on such pre-Hilbert spaces is given.

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  1. Institute of Mathematics, Jagiellonian University, ul. Łojasiewicza 6, 30-348, Kraków, Poland

    Piotr Niemiec

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  1. Piotr Niemiec
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Niemiec, P. Normal systems over ANR’s, rigid embeddings and nonseparable absorbing sets. Acta. Math. Sin.-English Ser. 28, 1531–1552 (2012). https://doi.org/10.1007/s10114-012-0709-8

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